This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality. Applications to function spaces and geometric measures are also presented. This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.
A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.
Discover data analytics methodologies for the diagnosis and prognosis of industrial systems under a unified random effects model In Industrial Data Analytics for Diagnosis and Prognosis - A Random Effects Modelling Approach, distinguished engineers Shiyu Zhou and Yong Chen deliver a rigorous and practical introduction to the random effects modeling approach for industrial system diagnosis and prognosis. In the book’s two parts, general statistical concepts and useful theory are described and explained, as are industrial diagnosis and prognosis methods. The accomplished authors describe and model fixed effects, random effects, and variation in univariate and multivariate datasets and cover the application of the random effects approach to diagnosis of variation sources in industrial processes. They offer a detailed performance comparison of different diagnosis methods before moving on to the application of the random effects approach to failure prognosis in industrial processes and systems. In addition to presenting the joint prognosis model, which integrates the survival regression model with the mixed effects regression model, the book also offers readers: A thorough introduction to describing variation of industrial data, including univariate and multivariate random variables and probability distributions Rigorous treatments of the diagnosis of variation sources using PCA pattern matching and the random effects model An exploration of extended mixed effects model, including mixture prior and Kalman filtering approach, for real time prognosis A detailed presentation of Gaussian process model as a flexible approach for the prediction of temporal degradation signals Ideal for senior year undergraduate students and postgraduate students in industrial, manufacturing, mechanical, and electrical engineering, Industrial Data Analytics for Diagnosis and Prognosis is also an indispensable guide for researchers and engineers interested in data analytics methods for system diagnosis and prognosis.
This volume constitutes the selected papers of the International Conference on Security Technology, SecTech 2009, held as part of the Future Generation Information Technology Conference, FGIT 2009, Jeju Island, Korea, in December 2009.
Non-Gaussian Signal Processing is a child of a technological push. It is evident that we are moving from an era of simple signal processing with relatively primitive electronic cir cuits to one in which digital processing systems, in a combined hardware-software configura. tion, are quite capable of implementing advanced mathematical and statistical procedures. Moreover, as these processing techniques become more sophisticated and powerful, the sharper resolution of the resulting system brings into question the classic distributional assumptions of Gaussianity for both noise and signal processes. This in turn opens the door to a fundamental reexamination of structure and inference methods for non-Gaussian sto chastic processes together with the application of such processes as models in the context of filtering, estimation, detection and signal extraction. Based on the premise that such a fun damental reexamination was timely, in 1981 the Office of Naval Research initiated a research effort in Non-Gaussian Signal Processing under the Selected Research Opportunities Program.
This proceedings volume convenes selected, peer-reviewed contributions presented at the POMS 2021 – International Conference on Production and Operations Management, which was virtually held in Lima, Peru, December 2-4, 2021. This book presents results in the field of Operations Management of key relevance to practitioners, instructors, and students. Topics focus on Operations Management, Logistics and Supply Chain Management, and Industrial and Production Engineering and Management, where mathematics and its applications play a role. In this work, readers will find a colorful collection of real-world case studies, accompanied by operations research-based managerial models. They touch on myriad topics, ranging from Artificial Intelligence and Data Analytics in Operations, Defense, Tourism, and other emerging issues in Operations Management to Healthcare Operations Management and Humanitarian Operations and Crisis Management. The POMS Lima 2021 International Conference has been organized by the Latin America & Caribbean Chapter of the Production and Operations Management Society, the most renowned professional and academic organization representing the interests of production and operations management professionals and academicians around the world. Since 2018, POMS International Conferences have been organized by POMS-LA, the first venue being in Rio de Janeiro, Brazil. Venue 2021 event was hosted by the Pontifical Catholic University of Peru and Pacific University, two Peruvian Latin-American leading academic institutions from Peru.
Various measures of information are discussed in first chapter. Information rate, entropy and mark off models are presented. Second and third chapter deals with source coding. Shannon's encoding algorithm, discrete communication channels, mutual information, Shannon's first theorem are also presented. Huffman coding and Shannon-Fano coding is also discussed. Continuous channels are discussed in fourth chapter. Channel coding theorem and channel capacity theorems are also presented. Block codes are discussed in chapter fifth, sixth and seventh. Linear block codes, Hamming codes, syndrome decoding is presented in detail. Structure and properties of cyclic codes, encoding and syndrome decoding for cyclic codes is also discussed. Additional cyclic codes such as RS codes, Golay codes, burst error correction is also discussed. Last chapter presents convolutional codes. Time domain, transform domain approach, code tree, code trellis, state diagram, Viterbi decoding is discussed in detail.
This book investigates the performance limitation issues in networked feedback systems. The fact that networked feedback systems consist of control and communication devices and systems calls for the integration of control theory and information theory. The primary contributions of this book lie in two aspects: the newly-proposed information-theoretic measures and the newly-discovered control performance limitations. We first propose a number of information notions to facilitate the analysis. Using those notions, classes of performance limitations of networked feedback systems, as well as state estimation systems, are then investigated. In general, the book presents a unique, cohesive treatment of performance limitation issues of networked feedback systems via an information-theoretic approach. This book is believed to be the first to treat the aforementioned subjects systematically and in a unified manner, offering a unique perspective differing from existing books.
